Need Help With Cartoon Eye Rig Rotation
The Lattice Object has its origin point outside the cage, not at the origin of the bone which it's parented to. So all rotations of the bone move the mesh around this origin point, not at its center. To fix this, do the following:

Select the Lattice Object in Object Mode.
From the menu, go to Object &gt; Set Origin &gt; Origin to Geometry
Shift+S &gt; Cursor to Selected.
Select the eye and the pupil, Shift+S &gt; Selection to Cursor.